Question

question 10

patricia was having fun playing a card game. to win the game, she needed the next two cards dealt to be yellow cards. there are 12 cards left in the deck, and three are yellow.

what is the probability that the two cards dealt to patricia will both be yellow?

\\(\frac{1}{24}\\)

\\(\frac{1}{22}\\)

\\(\frac{3}{44}\\)

\\(\frac{1}{4}\\)

Explanation:

Calculate first probability

Using the Dependent Events Probability knowledge point

$$ P(Y_1) = \frac{3}{12} $$

Calculate second probability

Using the Dependent Events Probability knowledge point

$$ P(Y_2 \mid Y_1) = \frac{2}{11} $$

Multiply the probabilities

Using the Dependent Events Probability knowledge point

$$ P(Y_1 \cap Y_2) = \frac{3}{12} \times \frac{2}{11} = \frac{6}{132} $$

Simplify the fraction

Using the Fraction Simplification knowledge point

$$ \frac{6}{132} = \frac{6 \div 6}{132 \div 6} = \frac{1}{22} $$

Answer:

• (A) \(\frac{1}{24}\)
• (B) \(\frac{1}{22}\) (Correct answer)
• (C) \(\frac{3}{44}\)
• (D) \(\frac{1}{4}\)